There are two numbers such that the sum of twice the first and thrice the second is 39, while the sum of thrice the first, and twice the second is 36. The larger of the two is :

Correct Answer: 3

Correct Answer: 8/11

Explanation:

Let the numerator be x Then, denominator =  x + 3.

Now. (x + 4)/(x + 3) +4 = 4/5  <=> 5 (x + 4) =  4(x + 7)

=>  x = 8.

The fraction is  8/11.

Correct Answer: 24

Explanation:

Let the ten's digit be x.

 

Then, unit's digit = x + 2.

 

Number = 10x + (x + 2) = 11x + 2

 

Sum of digits = x + (x + 2) = 2x + 2.

 

(11x + 2) (2x + 2) = 144

=> 22x^2+26x-140=0

 

=> (x - 2)(11x + 35) = 0

 

=> x = 2

 

Hence, Required Number = 11x + 2 = 24

Correct Answer: 400

Explanation:

Let the numbers be x and y.

 

Then, xy = 9375 and  x/y = 15.

 

x y x y = 9375 / 15

 

=> $$\begin{gathered} y 2 = 625 \\ \end{gathered}$$

 

=> y = 25

 

=> x = 15y = 15 x 25 = 375.

 

Sum of the numbers = 375 + 25 = 400.

Correct Answer: 270

Explanation:

Let the numbers be x and 1365+x

Then 1365+x = 6x+15 

=> x = 270

Correct Answer: 8, 4

Explanation:

Let the number of girls = x

=> x + x + 4 = 12

=> 2x = 8

=> x = 4

=> Number of girls = 4

=> Number of boys = 4 + 4 = 8

Correct Answer: 24 sqrt(10)

Explanation:

Let the numbers be x, x + 2 and X + 4.

Then, x(x + 2)(x +4) / 8 = 720 => x(x + 2)(x +4) = 5760.

?x  *  ?(x + 2) * ?(x +4) = ?x(x +2)(x + 4 ) = ?5760  =  24?10.

Correct Answer: 47.5

Correct Answer: 3/5

Explanation:

Let the required fraction be x/y. Then, x+1 / y+1 = 2 / 3 => 3x – 2y = - 1 …(i) and x – 1 / y – 1 = 1 / 2 2x – y = 1 …(ii) Solving (i) and (ii), x = 3 , y = 5 therefore, Required fraction= 3/5

Correct Answer: 13

Explanation:

(385/1001) = 5/13

First Number is 5

=> Fourth number is 13